Results 1 to 4 of 4

Math Help - triangular matrix

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    12

    triangular matrix

    if i have a matrix A how do i put it in upper triangular form??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    upper triangular form means that below the diagonal you have only zeros.

    to do that, you just need to apply elementary row operations to scale the matrix.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    Posts
    12
    arh let me refine my question if i have matrix A,

    PA(P^-1)=B , where B is upper triangular matrix, but what is P?

    i realised P contains eigenvectors as columns. but i stumble up as P has no inverse and it drives me mad and now im going to bed.
    Last edited by sheep99; May 1st 2009 at 02:43 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517
    Are you talking about finding the Jordan Canonical Form of the matrix? If your working over a field that contains all of the eigenvalues of the matrix (the complex numbers are algebraicly closed, so this is a good one to work in) you can represent the matrix into one that is zero everywhere except possibly the diagonal and 1st superdiagonal.

    The matrix P consists of the basis for the eigenspace of each of the Jordan blocks. In particular if you have all distinct eigenvalues, each eigenspace is one dimensional and your P matrix is just the corresponding eigenvectors and it will transform it into a diagonal matrix with the eigenvalues on the diagonal.

    Not really sure if this is what you are talking about, but hope it helps.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Upper triangular matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 14th 2011, 04:34 PM
  2. Replies: 2
    Last Post: January 18th 2011, 08:24 PM
  3. 4 by 4 triangular matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 12th 2010, 05:31 PM
  4. unitary and upper triangular matrix => diagonal matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 10th 2009, 06:52 PM
  5. Triangular Matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 27th 2009, 06:50 PM

Search Tags


/mathhelpforum @mathhelpforum